Noncommutative Analogs of Monomial Symmetric Functions, Cauchy Identity, and Hall Scalar Product

2007/12/13 by Tevlin, Lenny
#05A19 #05E05 #Combinatorics (math.CO) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.0712.2201

Abstract

This paper introduces noncommutative analogs of monomial symmetric functions and fundamental noncommutative symmetric functions. The expansion of ribbon Schur functions in both of these basis is nonnegative. With these functions at hand, one can derive a noncommutative Cauchy identity as well as study a noncommutative scalar product implied by Cauchy identity. This scalar product seems be the noncommutative analog of Hall scalar product in the commutative theory.

Related

• A Combinatorial Perspective on the Noncommutative Symmetric Functions
• Symmetric Functions in Noncommuting Variables
• Schur functions in noncommuting variables
• Noncommutative symmetric functions and skewing operators
• Noncommutative symmetric functions and quasi-symmetric functions with two and more paramters